1- The Imams have two positions. One is a personal position (father and brother) and one is an Imam. As a concerned father/brother, they say to their family: please don’t grieve over me too much. Don’t be depressed too much. It shows the Prophet’s/Imam’s humbleness and kindness. That’s like you saying to your wife and daughter: please don’t cry on me if I die. You don’t literally mean it. Obviously they will cry and lament. If they don’t cry and lament they are not humans. But as an Imam who was killed unjustly then they are obligated to cry a lot and reject that injustice.
2- We have tens of hadiths in Shia and Sunni sources that state the Prophet (s) cried on Imam Hussain (a).
3- We have many hadiths that urge us to show extreme sadness of Imam Hussain (a).
4- Imam Hussain (a) did not want Lady Zaynab (a) to look in front of those enemies, so he asked her not to do those things in front of those men. But doing them away from men it’s ok.
5- In Arab culture, if a woman would do that it could indicate she is not patient and rejects the will of God. The Imam did not want people to get such an impression.